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### Horngren'S Financial And Managerial Accounting

Book edition 6th
Author(s) Tracie L. Miller-Nobles, Brenda L. Mattison
Pages 992 pages
ISBN 9780134486833

# How is IRR calculated with unequal net cash inflows?

The after-tax cash flow for each period at time t is divided by some rate, r. The initial investment is then subtracted from the total of these discounted cash flows, yielding the present NPV. It is important to "reverse engineer" the value of r needed to make the NPV equal zero in order to determine the IRR.

See the step by step solution

## Step 1: Example

 years Net PV PresentCash factor valueInflow (i=16%) Net PV PresentCash factor valueInflow (i=18%) PV of each year’s inflow:1 (n=1)2 (n=2)3 (n=3)4 (n=4)5 (n=5)Total PV of cash inflows 0 Initial investment NPV $500,000 0.862$431,000 350,000 0.743 260,000 300,000 0.641 192,300 250,000 0.552 138,000 40,000 0.476 19,000 (1,040,390) 1,000,000) $40,390$500,000 0.847 $431,000 350,000 0.718 251,300 300,000 0.609 182,700 250,000 0.516 129,000 40,000 0.437 17,000 (1,003,980) (1,000,000)$3,980

In this example for 1,000,000 initial investment in a project and these irregular cashflows we can conclude that IRR for this project is 18%.

## Step 2: IRR advantage over NAV

NPV will be negative when IRR <cost of capital. Benefits: Since this strategy is expressed in percentage form, it is simple for financial managers to compare it to the necessary cost of capital.